The deadline-day signing came off the bench in the second half before firing a 96th-minute long-range strike to secure a 2-2 draw.
Maitland-Niles also praised the atmosphere at Hill Dickinson Stadium, claiming it was even better than Goodison Park.
The former Arsenal, Southampton and West Brom midfielder enjoyed a memorable start to life at Everton.
“It’s louder than Goodison – put it that way. And Goodison was really rocking when I was there. Goosebumps,” Maitland-Niles told Everton website.
“Words can’t describe how I feel.
“We’ve got the quality in our team to be able to win games, come up with draws, show fighting spirit.
“It’s a fighting team. From the first few days I entered the pitch with the rest of the team, you could see they’re fighters.
“If you’re not a fighter here, they won’t respect you. So, you have to earn your respect by fighting as much as they do – if not more.”